Pauli exclusion principles and Hund’s rule

Electrons

Electrons are the lightest of subatomic particles. Electrons have a mass, and they have a charge. An electron has a negative charge. Electrons have been in existence since the beginning of the universe. Since it is an electrical particle, it has mass. It is the lightest particle in the universe.

Tiny compared to protons and neutrons, over 1,800 times less than either a proton or a neutron. Electrons have a relative mass of 0.0005439 such that the electron is compared with the mass of a neutron being one or about 9.109×10-31 kg.

A proton is about 1836 times heavier than an electron, and a neutron’s mass is about 1840 times greater than an electron’s. Electrons are found in atoms near the nucleus, and they constantly move around the nucleus at speeds of thousands of metres per second. They have no electrical charge when alone, but they do become electrically charged when they bond with other atoms.

Pauli’s Exclusion Principle

Pauli’s Exclusion Principle is derived by analysing the mathematics of quantum mechanics and applies to all matter. It states that no two electrons in an atom can have the same four quantum numbers.

The electron has a spin that is always an integer, 0, 1/2, 1, 3/2, and so on. Electrons moving in orbits must obey the exclusion principle: No two electrons can be in the same quantum state. So if their orbits are at opposite ends of the atom, they belong to different shells.

That is not quite true. Although the shells have different energies, they don’t spin at different rates. They all spin at the same rate but with a different spin magnitude. Inside each shell, there are subshells with different quantum numbers of angular momentum, but all with the same total amount.

The upshot is that you can put two electrons into the same orbital if they have opposite spins: +1/2 and -1/2 for example. That means that it is possible to put two electrons into an orbital at one end of the atom and two more electrons into an orbital at the other end of the atom. In fact, this is what happens in sodium atoms when they form a crystal; after sodium, the vapour cools down to form sodium chloride (table salt).

Pauli’s exclusion principle forbids more than one fermion, such as an electron or a proton, from occupying the same quantum state at the same time. In particular, no two electrons in a molecule can have the same four quantum numbers: n, l, ml, and ms. Quantum mechanics thus predicts that these molecules will behave differently from those of other elements with chemically similar structures. The lightest element, hydrogen, is a case in point: it is composed of a single proton and a single electron. 

The next element up the periodic table is helium; its nucleus contains two protons and two neutrons bound together into a unit called a nucleus by the strong nuclear force. The helium atom has two electrons outside this nucleus, which obey Pauli’s exclusion principle and so fill different orbitals. Helium, therefore, has many properties like those of neon (the next element up the periodic table), even though their atoms are composed of different numbers of protons and neutrons.

Hydrogen fluoride is another example of how the Pauli exclusion principle explains differences between chemically similar molecules. HF is more than 99% lighter than HCl because its electrons are confined to separate 1s orbitals rather than having some in each orbital.

Hund’s Rule

Hund’s rule is named after the German chemist Adolf Hund, who first proposed it in 1925. In 1927, it was successfully used by Werner Heisenberg to explain the structure of the atom. For example, the electronic configuration of neon can be written as 1s22s22p6, which means that two electron fills up the ssubshell (the s subshell), then six electrons go into p-subshell (the second energy level) and finally ten electrons fill up the d-subshell (the third energy level).

In 1925, when Hund first proposed his rule, it did not attract much attention. But in 1927, when Heisenberg applied this rule to explain the atom in quantum theory, it became an important rule of quantum chemistry.

The basic idea behind Hund’s rule is very simple. It says that any time an electron jumps from one shell to another shell, an extra electron in the lower shell should be paired with it. The paired electrons must move in opposite directions because they are attracted to each other by the electrical force. 

Hund’s rule of maximum multiplicity states that for a given electronic configuration, the lowest energy term is the one with the greatest value of spin multiplicity.

A good example of this rule is the configuration of electrons in atoms and molecules. To understand how it works, consider the set of all possible configurations satisfying the octet rule for a given atom. Since there are two electrons per shell, and since inner shells can accommodate only two electrons, the total number of such configurations will be even (since each electron wants to be paired with another). As a result, each configuration has the same probability.

In calculations where one tries to predict the outcome of an experiment to find which state is more stable (more likely), Hund’s rule also plays an important role. This is achieved by using symmetry groups such as point groups or space groups in combination with Hund’s rule.

Conclusion

In this material, we discussed the concept of Pauli’s Extension principle and also the concept of Hund’s Rule. Hund’s rule is named after the German chemist Adolf Hund, who first proposed it in 1925. In 1927, it was successfully used by Werner Heisenberg to explain the structure of the atom.